Moving Charges and Magnetism · Question 33

Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly distributed across this cross-section. The distances from the centre of the wire’s cross-section at which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field, any where due to the wire, will be :

1. [a/2, 3a]
2. [a/4, 3a/2]
3. [a/2, 2a]
4. [a/4, 2a]

Answer

(3) [a/2, 2a]

Solution

By Ampere's circuital law:

Inside (r < a): B = 0 I r2 a2 (increases with r)

Outside (r > a): B = 0 I2 r (decreases with r)

Maximum field is at the surface: B = 0 I2 a

Inside: 0 I r2 a2 = 12 0 I2 a r = a2

Outside: 0 I2 r = 12 0 I2 a r = 2a

[a/2, 2a]

Answer: (3)